BRODERICK, J.

The defendant, Delvin White, appeals his convictions following a jury trial of one count of aggravated felonious sexual assault, see RSA 632-A:2, II (1996) (amended 1997, 1998, 1999), and two counts of felonious sexual assault, see RSA 632-A:3 (1996) (amended 1997). He contends that the Superior Court (Barry, J.) erred by: (1) excluding the victims' prior allegations of sexual assault against other individuals; (2) admitting hearsay statements by the victims to an emergency room physician; (3) excluding evidence that the victims had previously been placed in foster care; and (4) sentencing him to an extended term of incarceration under RSA 651:6 (1996) (amended 1996, 1997, 1998, 1999). We affirm the defendant's convictions, vacate the sentence, and remand for resentencing.

The following facts were either adduced at trial or are undisputed. In March 1996, the defendant spent an afternoon visiting a friend and his girlfriend at their apartment in Manchester. The friend had two daughters, ages twelve and eight, and the girlfriend had two sons, all of whom were together at the apartment that day. After spending the afternoon playing cribbage, listening to the radio, and drinking beer with his friend, the defendant accepted an invitation to stay for dinner. It was later agreed that he would spend the night.

At trial, the younger daughter testified that while she sat with the defendant on a day bed watching television, he rubbed her breasts, put his hands down her pants, and "stuck his finger in." When the daughter told her father what had happened, he attacked the defendant. During this confrontation, the older daughter came out of a bedroom crying hysterically. She later related that earlier that same day the defendant had touched her breasts, her vaginal area, and inserted his finger in her "private." As the confrontation between the father and the defendant continued, the father's girlfriend took all of the children to a neighbor's apartment and called the police. After an investigation, the police told her to take the victims to the hospital for a physical examination, and she did so.

The defendant was convicted of aggravated felonious sexual assault against the older child and one count of felonious sexual assault against each child. This appeal followed.

I

The defendant argues that the trial court erred in excluding evidence of the victims' prior allegations of sexual assault against other individuals. He contends that these prior allegations were false, and therefore admissible to impeach the victims' credibility. See N.H. R. Ev. 608(b).

"The admissibility of evidence is a matter within the trial court's broad discretion, and we will not upset [its] ruling absent an abuse of that discretion." State v. Dewitt, 143 N.H. 24, 26-27, 719 A.2d 570, 572 (1998). Here, the probative value of the victims' prior allegations of sexual assault against other individuals depends upon their truthfulness. If the prior allegations were false, they would adversely affect the victims' credibility. See State v. Dukette, 127 N.H. 540, 549, 506 A.2d 699, 706 (1986). The trial court refused to admit the prior allegations, however, because the defendant "failed to persuade [it] that any of [the victims'] prior allegations . . . were demonstrably false." We must first decide whether "demonstrably false" is the proper standard to be applied. Cf. State v. Walters, 142 N.H. 239, 242, 698 A.2d 1244, 1246 (1997) ("The party offering evidence generally bears the burden of demonstrating its admissibility.").

The defendant argues that a less stringent standard controls, asserting that prior allegations of sexual assault should be admitted if there is a "reasonable probability" they are false. See Clinebell v. Com., 368 S.E.2d 263, 266 (Va. 1988). We disagree. This standard, if adopted, could "divert the attention of the trial from its primary objective [of] determini[ng] . . . the guilt or innocence of [an] accused . . . [and] in effect [put] the complainant on trial as to the truthfulness of any complaint [of sexual assault]." State v. Johnson, 692 P.2d 35, 43 (N.M.Ct.App. 1984), overruled in part on other grounds by Manlove v. Sullivan, 775 P.2d 237 (N.M. 1989).

The State invites us to adopt the "demonstrably false" standard, but to construe it as meaning false "in fact." See, e.g., State v. Hutchinson, 688 P.2d 209, 212-13 (Ariz.Ct.App. 1984); Com. v. Bohannon, 378 N.E.2d 987, 991 (Mass. 1978). The pitfall of this heightened approach is that there are few, if any, situations where the standard could be met, other than where the victim testifies to the falsity of the prior allegations. Accordingly, we reject the State's invitation. Instead, we hold that the trial court correctly determined that a defendant may introduce a victim's prior allegations of sexual assault by showing that the prior allegations were demonstrably false, which we interpret to mean "clearly and convincingly untrue." This approach requires greater proof of falsity than the "reasonable probability" standard proposed by the defendant, but less certitude than the "false-in-fact" test offered by the State. It also ensures that there will not be a "trial within a trial" on evidence ultimately excluded while still allowing a defendant the opportunity to present relevant evidence.

A

We must now decide whether the trial court properly applied the standard. Both victims previously accused a neighbor of committing sexual assault, but he was eventually acquitted of the charges. The defendant contends that the acquittal, in conjunction with other proffered evidence, satisfies his proof. We disagree. While an acquittal is strong evidence that the jury may have found a victim's allegations to be unreliable, an acquittal, by itself, does not necessarily clearly and convincingly demonstrate that the victims were lying about the assaults. Rather, an acquittal merely means that the State failed to carry its burden of proving beyond a reasonable doubt one or more elements of the charged crime. See United States v. Kerley, 643 F.2d 299, 300-01 (5th Cir. 1981). Such failure can result from a variety of factors. See United States v. Hernandez, 146 F.3d 30, 33 n. 1 (1st Cir. 1998).

The defendant also relies on testimony at the neighbor's trial from the victims' babysitter and their mother's then boyfriend as elements of the clear and convincing proof of the falsity of the older victim's prior allegation of sexual assault. The babysitter testified that she heard the older victim tell her mother that her accusations were not true. The former boyfriend testified that the older victim told him she was lying when she accused the neighbor of sexual assault. The trial court in the present case, however, was not persuaded by the babysitter's testimony because it did "not find [her] testimony credible given the State's offers of inconsistency and questionable credibility." The defendant contends that the trial court erred by taking the issue of the babysitter's credibility from the jury, instead relying on the State's "unsubstantiated" proffer to determine the babysitter's threshold credibility.

We agree that credibility is normally a matter for the trier of fact. See State v. Lowe, 140 N.H. 271, 275, 665 A.2d 740, 743 (1995). The trial court, however, must make an initial determination of credibility or else risk admitting evidence of prior allegations without a showing that they are demonstrably false, resulting in a "trial within a trial" and confusing the jury. See N.H. R. Ev. 104(a); State v. Alexander, 143 N.H. 216, 221-22, 723 A.2d 22, 26 (1998). At the hearing on the defendant's motion in limine, the State proffered that the babysitter was unreliable, stating that she had provided "multiple statements" concerning the older victim's allegations, including statements that she could not remember the pertinent events. The State contended that her memory loss was due to, inter alia, cocaine addiction. "We [have previously] acknowledge[d] that a proffer of evidence presents a great risk of an erroneous pretrial ruling." State v. Haley, 141 N.H. 541, 544, 689 A.2d 671, 674 (1997). Here, however, the trial court had not only the State's proffer, but also the entire transcript of the babysitter's testimony from the neighbor's trial. Although we do not have the entire transcript before us, we do have portions which suggest a possible bias on the part of the babysitter in favor of the neighbor accused of sexual assault. We assume that the trial court examined the entire transcript before deciding that the defendant had not shown the prior allegations of sexual assault to be demonstrably false. See Brown v. John Hancock Mut. Life Ins. Co., 131 N.H. 485, 492-93, 558 A.2d 822, 826 (1989). We cannot say, therefore, that the trial court abused its discretion in finding that the babysitter's testimony at the neighbor's trial did not satisfy the defendant's burden of establishing falsity.

The trial court also excluded the former boyfriend's testimony that the older victim had recanted her accusations of sexual assault against the neighbor because the "recantation was made under circumstances akin to duress or coercion." The defendant challenges this decision because the former boyfriend "testified at [the neighbor's] trial that the recantation did not result from any coercion." Notwithstanding this testimony, the trial court could have reasonably found, based on the transcript of the former boyfriend's testimony, that he was in fact coercing the older victim to recant. Cf. State v. Berry, 117 N.H. 352, 355, 373 A.2d 355, 357 (1977) (conflicts in evidence for trier of fact).

The defendant next alleges that the older victim's prior allegations against her cousin of sexual assault should have been admitted. He relies upon the fact that the police closed their investigation into the alleged assault due to reasonable doubt. Further, the babysitter had testified during the neighbor's trial that the older victim admitted to her that she lied in accusing her cousin of assault. The failure of the police to arrest due to lack of probable cause does not demonstrate clearly and convincingly the falsity of the allegations. Cf. Com. v. Hicks, 503 N.E.2d 969, 972-73 (Mass.Ct.App. 1987) (that charges were dropped at the request of the victim not a sufficient basis for inferring that those charges were false). For the reasons discussed earlier, we find that the trial court did not abuse its discretion in finding the babysitter's testimony lacking in credibility. Accordingly, the trial court did not err in excluding evidence of the older victim's prior allegations against her cousin.

The defendant also contends that the older victim's prior allegation of sexual assault against an individual named "Mac" or "Uncle Mack" should have been admitted to impeach her credibility. The defendant points only to the fact that the "police were unable to identify `Mac'" as evidence that the allegation was false. We note that the statement that the police were "unable to identify any person with the first name of Mac (last name unknown)" was contained in an investigative report on the older victim's allegations of sexual assault against her cousin. Further, the older victim's allegation against her cousin also included her belief that "Mac" or "Uncle Mack" was now deceased. The failure of the police to identify the alleged perpetrator of one sexual assault while investigating a different sexual assault, when the police have only a first name and the alleged perpetrator is reportedly deceased, does not demonstrate clearly and convincingly that the older victim was lying about the assault.

Finally, the defendant argues that the younger victim's prior allegations of sexual assault against the neighbor were false because her description of the assault varied over the course of a year. Her story did, however, remain consistent about where she was touched. The State contends that the defendant did not preserve this argument for appeal. Assuming, without deciding, that this issue was properly preserved for appeal, we do not find an abuse of discretion in the trial court's finding. That a five-year-old child's story concerning an alleged sexual assault varied somewhat over the course of one year concerning one aspect of the assault did not demonstrate clearly and convincingly that the allegations were false. See State v. Cressey, 137 N.H. 402, 411-12, 628 A.2d 696, 702-03 (1993).

We find no error by the trial court in denying the admission of these individual pieces of evidence as to the falsity of the prior allegations. Consequently, we reject the defendant's argument that the cumulative effect of the prior allegations demonstrated their falsity. See State v. Smart, 136 N.H. 639, 669, 622 A.2d 1197, 1216 (1993). Here, the whole is simply not greater than the sum of its parts. Although the number of prior allegations made by the victims in this case may give pause, a contrary holding would mean that even if a defendant failed to demonstrate clearly and convincingly that discrete prior allegations were false, he could still introduce them by merely pointing to their sheer number. If, as argued by the defendant, the correct standard for admissibility of prior allegations were "reasonable probability of falsity," we agree that the defendant would have met that standard in this case. Where the proper standard is "demonstrably false," however, and where the defendant must introduce evidence which "clearly and convincingly" shows the prior allegations to be demonstrably false, the defendant has simply not met this higher standard. While the quantity of evidence may be of some value, it is the quality of that evidence that is paramount. Here, had the defendant's pieces of proffered evidence been of a higher quality, the defendant may very well have met the "demonstrably false" standard. Given the questionable nature of the evidence presented, however, the defendant's motion must fail.

B

Alternatively, the defendant argues that the prior allegations were admissible to show the victims' prior sexual knowledge. The defendant contends that the older victim's allegations against "Mac" and the younger victim's allegations against the neighbor were sufficiently similar to their allegations against the defendant to be admissible to show an alternative source for the victims' sexual knowledge.

"Trial courts have broad discretion in determining the scope of cross-examination and we will not overturn the trial court's ruling absent an abuse of that discretion." State v. Ellsworth, 142 N.H. 710, 720, 709 A.2d 768, 774 (1993) (quotation omitted). Prior sexual assault can be relevant to demonstrate that the victims' knowledge came not from the charged acts, but from prior sexual assault inflicted by another. See id.

We agree that similarities exist between the prior allegations and the allegations at issue in this case. At the hearing on the defendant's motion in limine, however, the State presented testimony from the victims' pediatrician and social worker to demonstrate that the source of their sexual knowledge was not from earlier sexual assaults, but was from counseling and physical examinations.

The victims' pediatrician had given them physical examinations since 1993. The doctor testified that she told them that certain parts of their bodies are special and asked them what they would do if anyone ever touched them there. She then testified that she told the victims

[T]hat is your own special place. Nobody has a right to touch you down there with their fingers or with their penis and if this were to occur, then it is your right to say, get away from me and I'm going to go tell so and so.

The social worker testified that she had conversations with the victims about sexual victimization, "good touching" versus "bad touching," and "that there are certain things that nobody should be doing with them." She instructed them regarding "[w]hat the certain parts of their body are that are private." Given the knowledge that the victims obtained from the pediatrician and the social worker, we cannot conclude that the trial court abused its discretion in finding the proffered evidence inadmissible because the victims' prior knowledge could have been derived from these sessions and not from prior sexual assault. See id. at 721, 709 A.2d at 775.

The defendant contends that although the trial court may have satisfied itself that the victims obtained their sexual knowledge elsewhere, the jury did not know this because the trial court did not require the State to present this testimony. The trial court's initial order on the admissibility of the prior sexual assaults did appear to require the State to present the testimony of these two witnesses in order to establish alternative means for the victims' prior sexual knowledge. The trial court, however, clarified its order, stating

Just to make that clear, when I wrote that, I anticipated that the defense was going to mount a challenge as to the sexual knowledge of these girls and how it was obtained, that's why I said that. It wasn't creating an unequivocal burden for the State to meet in addition to proving each one of the allegations beyond a reasonable doubt.

The State had no duty to present these witnesses; it was simply required to prove each element of the crime charged beyond a reasonable doubt. See State v. Parker, 142 N.H. 319, 322, 702 A.2d 306, 308 (1997).

C

The defendant argues that his right to present all favorable proofs under Part I, Article 15 of the New Hampshire Constitution and the Sixth Amendment to the United States Constitution was violated by his inability to impeach the victims' credibility by using their prior allegations of sexual assaults. "The New Hampshire Constitution is at least as protective as the Federal Constitution in this area, and we therefore decide this case under the State Constitution, employing federal cases to aid in our analysis." State v. Graf, 143 N.H. 294, 296, 726 A.2d 1270, 1273 (1999) (quotation omitted). "Both the Compulsory Process Clause of the Federal Constitution and the right to produce all favorable proofs under Part I, Article 15 give a defendant only the right to produce witnesses, not to produce their testimony." Id. The defendant does not argue that he was prevented from producing the victims as witnesses, therefore his argument that the trial court violated his right to present all favorable proofs is without merit. See id.

The defendant also contends that the trial court violated his State and Federal constitutional due process rights and right to confront witnesses by not permitting him to cross-examine the victims regarding their prior allegations. We will first address the defendant's claim under the State Constitution, see State v. Ball, 124 N.H. 226, 231, 471 A.2d 347, 350 (1983), and will engage in a separate federal analysis only if federal law is more favorable. See State v. Seymour, 140 N.H. 736, 742, 673 A.2d 786, 791 (1996).

We previously have found no State constitutional violation in the context of Rule 608(b) where "the defendant has failed to make a threshold showing of probity and similarity." Ellsworth, 142 N.H. at 719, 709 A.2d at 774. In the instant case, the prior allegations of sexual assault are not probative of the victims' motives because, as discussed above, the defendant has failed to demonstrate clearly and convincingly that the prior allegations are false. Because federal law does not provide any additional protection in this area, we need not undertake a separate federal analysis. See id. at 719-20, 709 A.2d at 774; Clinebell, 368 S.E.2d at 266 (while Sixth Amendment of Federal Constitution gives the defendant the right to cross-examine complainant about prior allegations, the defendant must still demonstrate that the prior allegations were false).

II

The defendant next challenges the testimony of the emergency room physician who examined the children and recounted what each said about the assaults. Specifically, the doctor said both children told him that a male house guest "put his hand down in [their] shirt[s] and had his hand in [their] pants." The defendant contends that this testimony was inadmissible hearsay because the victims' statements: (1) were not made with the intent of receiving medical diagnosis or treatment; (2) were not reasonably pertinent to a medical diagnosis or treatment; and (3) were not made under circumstances indicating that the statements were trustworthy.

New Hampshire Rule of Evidence 803(4) excepts from the hearsay rule

[s]tatements made for purposes of medical diagnosis or treatment and describing medical history, or past or present symptoms, pain, or sensations, or the inception or general character of the cause or external source thereof insofar as reasonably pertinent to diagnosis or treatment, regardless of to whom the statements are made, or when the statements are made, if the court, in its discretion, affirmatively finds that the proffered statements were made under circumstances indicating their trustworthiness.

The trial court's preliminary factual determinations for admissibility under Rule 803(4) will be upheld unless clearly erroneous, see State v. Roberts, 136 N.H. 731, 738-40, 622 A.2d 1225, 1230-32 (1993), and absent an abuse of discretion, we will uphold the trial court's determination that Rule 803(4) evidence should be admitted. See State v. Young, 144 N.H. 477, 482, 743 A.2d 1275, 1280 (1999); United States v. Bailey, 581 F.2d 341, 346 (3d Cir. 1978).

"We examine three areas of inquiry in determining the admissibility of evidence under Rule 803(4): the declarant's intent; the subject matter of the statements; and whether there are circumstances indicating the trustworthiness of the statements." Graf, 143 N.H. at 303, 726 A.2d at 1277-78 (quotation omitted).

We first address the intent of the two children in making the statement to the examining emergency room physician. When the declarant is a child, "[t]he proponent of Rule 803(4) statements must present evidence establishing that the child had the requisite intent, by showing that the child made the statements understanding that they would further the diagnosis and possible treatment of the child's condition." Id. at 303-04, 726 A.2d at 1278 (quotation omitted). While we have required affirmative evidence on the record of a child declarant's intent, see State v. Wade, 136 N.H. 750, 755, 622 A.2d 832, 835 (1993), this intent can be established by circumstantial evidence. See Lowe, 140 N.H. at 273, 665 A.2d at 742. Express testimony from the victims about their intent is not necessary. See Graf, 143 N.H. at 303-04, 726 A.2d at 1278.

The defendant contends that the State failed to establish that the victims possessed the requisite intent because they were told by the doctor that the examination was done to prepare an evidence kit. The mere fact that the doctor explained that he was going to examine and collect evidence for an evidence kit does not mean that the victims did not also understand that the doctor was going to treat them. After hearing the complaints of the victims, the doctor conducted an examination that had the dual purpose of treatment and evidence collection. When determining a child's intent, one must look at all the surrounding facts and circumstances. See State v. Stinnett, 958 S.W.2d 329, 331 (Tenn. 1997). The victims were taken to the hospital hours after the defendant allegedly assaulted them. The older victim complained of pain and the younger victim was visibly upset as a result of the alleged assaults. The temporal proximity between the victims' complaints, their emotional upheaval, and the visit to the hospital supports a finding that the victims knew the reason for the visit related to their physical and emotional health. See Lowe, 140 N.H. at 273-74, 665 A.2d at 742. At their respective ages, the victims would have understood that the purpose of a hospital emergency room is medical treatment. See Stinnett, 958 S.W.2d at 332. Unlike the circumstances present in State v. Woods, 130 N.H. 721, 729, 546 A.2d 1073, 1078 (1988), there was no evidence here that the sole purpose of the examination was to collect evidence. Therefore, the trial court did not abuse its discretion in finding that the victims' statements were made with the intent of receiving medical treatment.

The defendant next argues that the victims' statements about the assaults were not pertinent to medical diagnosis or treatment. This argument is without merit. As the doctor testified, the victims' descriptions of the assaults structured the physical examination. See People v. McElhaney, 545 N.W.2d 18, 26 (Mich.Ct.App. 1996). Depending on the nature of the sexual assault inflicted on the victims, the doctor would have treated them for different ailments and possible diseases. Therefore, the victims' complaints were in fact pertinent to medical diagnosis or treatment. See State v. Kay, 927 P.2d 897, 909 (Idaho Ct. App. 1996).

The defendant also contends that the trial court erred in admitting the doctor's testimony because there were no circumstances indicating that the victims' statements were trustworthy. We have held that statements made to a physician are trustworthy, in part, because of the duration of the relationship between the doctor and patient. See Lowe, 140 N.H. at 275, 665 A.2d at 743. That does not mean, however, that the victims' statements here are untrustworthy merely because the victims had not been seen previously by the emergency room doctor. The doctor interviewed the victims separately. Both victims cooperated with the examinations, see Graf, 143 N.H. at 304, 726 A.2d at 1278, and answered questions on their own without prompting. The doctor testified that the victims maintained good eye contact with him. Although their father's girlfriend was present, the victims were neither prompted by her nor did they look to her for answers to the doctor's questions. Accordingly, we conclude that the trial court's determination that the doctor's testimony met the three prongs of Rule 803(4) was not clearly erroneous. Therefore, the trial court did not abuse its discretion in admitting the doctor's testimony under Rule 803(4).

III

The defendant alleges that the trial court erred by excluding evidence that the victims had previously been placed in foster care. Part of the defendant's theory as to why the victims were motivated to fabricate the allegations of assault was because they were afraid that their father, who had been incarcerated as a habitual offender, would be imprisoned again as he had resumed drinking, resulting in another foster care placement for the victims. On the day of the sexual assaults, the victims' father and the defendant drank a case of beer together. The court admitted evidence of the father's previous incarceration after finding that there was "a nexus between [the father's] incarceration and the defendant's claim that the children fabricated the charges against [him] to get attention so that [their father] would stop drinking." The court excluded evidence of the victims' previous placement in foster care because it did not find the existence of a similar nexus.

"The determination of the relevance of evidence is a matter for the trial court's sound discretion, and we will not overturn such a determination absent an abuse of discretion." State v. Graham, 142 N.H. 357, 362, 702 A.2d 322, 325 (1997). In order to demonstrate an abuse of discretion, the defendant must show that the court's decision "was clearly untenable or unreasonable to the prejudice of his case." Id. (quotation omitted). There was no evidence that the victims feared their father's renewed drinking would result in another foster care placement. When the victims had been placed in foster care previously, their mother was a drug user and unable to care for them. At the time of the sexual assaults, the father had resumed drinking approximately four months earlier, but the mother no longer used drugs and she had custody of one of the victims. The father's drinking, therefore, was unlikely to lead to their renewed placement in foster care. We cannot say that the trial court abused its discretion by excluding evidence of the victims' previous foster care placement after finding no nexus between the foster care placement and a motive to fabricate the charges of sexual assault.

IV

Finally, the defendant contends that the trial court erred in sentencing him to an extended term under RSA 651:6, I(c), II(d) (1996). The State concedes that this was error. We therefore vacate the sentence and remand for resentencing.

Convictions affirmed; sentence vacated; remanded for resentencing.

JOHNSON, J., sat for oral argument but retired prior to the final vote; THAYER, J., sat for oral argument but resigned prior to the final vote; BROCK, C.J., concurred; HORTON, J., retired, specially assigned under RSA 490:3, concurred.